Measurement of the spatial correlation function of phase fluctuating Bose-Einstein condensates.

We measure the intensity correlation function of two interfering spatially displaced copies of phase fluctuating Bose-Einstein condensates. It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated condensates. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.